Fourier Ptychography Research Articles

Addressing phase-curvature in Fourier ptychography.

In Fourier ptychography, multiple low resolution images are captured and subsequently combined computationally into a high-resolution, large-field of view micrograph. A theoretical image-formation model based on the assumption of plane-wave illumination from various directions is commonly used, to stitch together the captured information into a high synthetic aperture. The underlying far-field (Fraunhofer) diffraction assumption connects the source, sample, and pupil planes by Fourier transforms. While computationally simple, this assumption neglects phase-curvature due to non-planar illumination from point sources as well as phase-curvature from finite-conjugate microscopes (e.g., using a single-lens for image-formation). We describe a simple, efficient, and accurate extension of Fourier ptychography by embedding the effect of phase-curvature into the underlying forward model. With the improved forward model proposed here, quantitative phase reconstruction is possible even for wide fields-of-views and without the need of image segmentation. Lastly, the proposed method is computationally efficient, requiring only two multiplications: prior and following the reconstruction.

Pose correction scheme for camera-scanning Fourier ptychography based on camera calibration and homography transform.

Fourier ptychography (FP), as a computational imaging method, is a powerful tool to improve imaging resolution. Camera-scanning Fourier ptychography extends the application of FP from micro to macro creatively. Due to the non-ideal scanning of the camera driven by the mechanical translation stage, the pose error of the camera occurs, greatly degrading the reconstruction quality, while a precise translation stage is expensive and not suitable for wide-range imaging. Here, to improve the imaging performance of camera-scanning Fourier ptychography, we propose a pose correction scheme based on camera calibration and homography transform approaches. The scheme realizes the accurate alignment of data set and location error correction in the frequency domain. Simulation and experimental results demonstrate this method can optimize the reconstruction results and realize high-quality imaging effectively. Combined with the feature recognition algorithm, the scheme provides the possibility for applying FP in remote sensing imaging and space imaging.

Implementation of free-space Fourier Ptychography with near maximum system numerical aperture.

Over the past decade, the research field of Fourier Ptychographic Microscopy (FPM) has seen numerous innovative developments that significantly expands its utility. Here, we report a high numerical aperture (NA) FPM implementation that incorporates some of these innovations to achieve a synthetic NA of 1.9 - close to the maximum possible synthetic NA of 2 for a free space FPM system. At this high synthetic NA, we experimentally found that it is vital to homogenize the illumination field in order to achieve the best resolution. Our FPM implementation has a full pitch resolution of 266 nm for 465 nm light, and depth of field of 3.6 µm. In comparison, a standard transmission microscope (incoherent) with close to maximum possible NA of 0.95 has a full pitch resolution of 318 nm for 465 nm light, and depth of field of 0.65 µm. While it is generally assumed that a free-space coherent imaging system and a free-space incoherent imaging system operating at their respective maximum NA should give comparable resolution, we experimentally find that an FPM system significantly outperforms its incoherent standard microscopy counterpart in resolution by a factor of 20%. Coupled with FPM's substantially longer effective depth of field (5.5 times longer), our work indicates that, in the near-maximum NA operation regime, the FPM has significant resolution and depth of field advantages over incoherent standard microscopy.

Experimental Study on the Exploration of Camera Scanning Reflective Fourier Ptychography Technology for Far-Field Imaging

Fourier ptychography imaging is a powerful phase retrieval method that can be used to realize super-resolution. In this study, we establish a mathematical model of long-distance camera scanning based on reflective Fourier ptychography imaging. In order to guarantee the effective recovery of a high-resolution image in the experiment, we analyze the influence of laser coherence in different modes and the surface properties of diverse materials for diffused targets. For the analysis, we choose a single-mode fiber laser as the illumination source and metal materials with high diffused reflectivity as the experimental targets to ensure the validity of the experimental results. Based on the above, we emulate camera scanning with a single camera attached to an X-Y translation stage, and an experimental system with a working distance of 3310 mm is used as an example to image a fifty-cent coin. We also perform speckle analysis for rough targets and calculate the average speckle size using a normalized autocorrelation function in different positions. The method of calculating the average speckle size for everyday objects provides the premise for subsequent research on image quality evaluation; meanwhile, the coherence of the light field and the targets with high reflectivity under this experiment provide an application direction for the further development of the technique, such as computer vision, surveillance and remote sensing.

Double optical image encryption system based on near-field Fourier ptychography

This paper proposes a double encryption system based on near-field Fourier ptychography (FP). Firstly, the encryption and decryption processes of a complex-amplitude image are realized by the principle of near-field FP while improving the imaging system. Our method uses a spatial light modulator to apply a phase shift to the object in the frequency domain to control the displacement of the object in the spatial domain, avoiding systematic errors caused by mechanically moving object. The second encryption process is designed by further utilizing the characteristics of the imaging system and can recover the object and the illumination pattern at the same time, which can decrypt another image from the object and illumination pattern recovered above. Since the second encryption is harder to be detected by the attacker, it has higher concealment and security. Finally, numerical simulations verify the feasibility, security and robustness of the proposed encryption system.

Performance comparison of wavelet families for noise reduction and intensity thresholding in Fourier Ptychographic microscopy

Microscopy is going through a digital renaissance and new schemes are developed where computer and algorithms constitute an integral part of the imaging process itself. Computational microscopy increases performance by offering better resolution, larger field of view, quantitative contrast and also reduced size, weight and economic cost. Fourier Ptychographic microscopy utilizes multiple images of a sample taken at lower resolution, each illuminated with a unique incidence angle coherent source, and synthesizes one high resolution complex valued image by iterative phase retrieval algorithms. The recorded images are often corrupted with background noise and pre-processing is needed to improve the quality of the FP recovered image. The pre-processing involves data denoising, thresholding and intensity balancing. We have investigated different wavelet families to test their performance in terms of having compact support and giving the desired level of decomposition for optimal intensity thresholding and denoising in Fourier Ptychography (FP). The wavelet families Daubechies, Biorthogonal, Reverse Biorthogonal, Coiflet, Fejer-Korovkin, Discrete Meyer and Symlet with different compact support have been studied. The obtained threshold was used with noisy synthetic and experimental images for a variety of objects to evaluate the performance of the described framework. In particular, Reverse Biorthogonal wavelets were found to preserve useful signal in corrupted images to a great extent (RMS error 0.39) with low computational cost. Consequently, quantitatively more correct amplitude and phase images with uniform and homogeneous background could be recovered.

Introduction to Fourier Ptychography: Part I

Abstract:Fourier ptychography is an emerging computational microscopy technique that can generate gigapixel-scale images of biological samples. With only the addition of a low-cost LED array to a standard digital microscope and a reconstruction algorithm, Fourier ptychography overcomes the fundamental trade-off between a microscope's resolution and field-of-view without any moving parts. This article is the first in a three-part series that aims to introduce the fundamentals of the technology to the broader microscopy community and beyond, using intuitive explanations.

Dictionary-based compressive Fourier ptychography.

Fourier ptychography (FP) provides an alternative scheme for improving the spatial bandwidth product with limited device. However, an angle-variation illumination is necessary to realize scanning imaging in the Fourier plane, which dramatically restricts the imaging speed and detection efficiency. In this paper, we propose a multiplexing and compressible FP scheme based on the structured illuminations and compressive sensing technique. Half of the LEDs are lighted together to reduce the exposure time; meanwhile, a learned dictionary is employed to reduce the sampling times. In addition, spectral independent illumination is proposed to retrieve color information from monochrome samplings. We experimentally verify that the proposed method can effectively reduce the sampling time with limited resolution loss.

Resolution enhancement of long-range imaging with sparse apertures

Synthetic aperture technique could effectively expand the passband and beyond the diffraction limit of aperture. Macroscopic Fourier ptychography (FP) makes synthetic aperture feasible in visible light by incorporating phase retrieval process into synthetic aperture. In FP, a dense aperture sampling is necessary to overcome the ill-posedness of phase retrieval, which leads to long acquisition time and heavy computation. Here, a total variation regularization-based Fourier ptychographic (TVFP) reconstruction method is proposed for long-range imaging. The TVFP method imposes total variation constraints to improve the ill-posedness of the imaging model, and recovers high-quality image from sparse aperture sampling. For the imaging system with aberration, a joint optimization of pupil function and target image is also proposed to achieve the aberration free image and the estimated pupil function simultaneously. The results show the aperture overlapping ratio could be reduced to 25% or less. The proposed method simplifies the imaging configuration and improves the robustness for long-range imaging.

Fourier ptychography multi-parameunter neural network with composite physical priori optimization.

Fourier ptychography microscopy(FPM) is a recently developed computational imaging approach for microscopic super-resolution imaging. By turning on each light-emitting-diode (LED) located on different position on the LED array sequentially and acquiring the corresponding images that contain different spatial frequency components, high spatial resolution and quantitative phase imaging can be achieved in the case of large field-of-view. Nevertheless, FPM has high requirements for the system construction and data acquisition processes, such as precise LEDs position, accurate focusing and appropriate exposure time, which brings many limitations to its practical applications. In this paper, inspired by artificial neural network, we propose a Fourier ptychography multi-parameter neural network (FPMN) with composite physical prior optimization. A hybrid parameter determination strategy combining physical imaging model and data-driven network training is proposed to recover the multi layers of the network corresponding to different physical parameters, including sample complex function, system pupil function, defocus distance, LED array position deviation and illumination intensity fluctuation, etc. Among these parameters, LED array position deviation is recovered based on the features of brightfield to darkfield transition low-resolution images while the others are recovered in the process of training of the neural network. The feasibility and effectiveness of FPMN are verified through simulations and actual experiments. Therefore FPMN can evidently reduce the requirement for practical applications of FPM.

Phase Diversity-Based Fourier Ptychography for Varying Aberration Correction

Fourier ptychography (FP) is geared toward high-resolution imaging with a large field of view efficiently. In the original illumination-based FP scheme, the aberrations in optical systems can be well reconstructed, which plays a prominent role in simple and compact optical arrangements. Unfortunately, the reconstruction strategy for recovering an optical system’s pupil function fails to carefully consider the nature of the field-dependent pupil function in the aperture-scanning FP scheme, which affects the quality of the reconstructed image to a certain extent. Based on this observation, we report a phase diversity-based FP (PDFP) scheme for varying aberration correction. We image USAF resolution target with the proposed PDFP scheme and demonstrate our ability to correct varying aberration and improve image quality. The reported approach allows aperture-scanning FP technology to use simpler optical systems for imaging and may facilitate the further development of FP in practical applications such as industrial inspection and long-distance imaging.

High-resolution 3D Fourier ptychographic reconstruction using a hemispherical illumination source with multiplexed-coded strategy.

Fourier ptychography is a promising and flexible imaging technique that can achieve 2D quantitative reconstruction with higher resolution beyond the limitation of the system. Meanwhile, by using different imaging models, the same platform can be applied to achieve 3D refractive index reconstruction. To improve the illumination NA as much as possible while reducing the intensity attenuation problem caused by the LED board used in the traditional FP platform, we apply a hemispherical lighting structure and design a new LED arrangement according to 3D Fourier diffraction theory. Therefore, we could obtain the illumination of 0.98NA using 187 LEDs and achieve imaging half-pitch resolutions of ∼174 nm and ∼524 nm for the lateral and axial directions respectively, using a 40×/0.6NA objective lens. Furthermore, to reduce the number of captured images required and realize real-time data collection, we apply the multiplexed-coded illumination strategy and compare several coded patterns through simulation and experiment. Through comparison, we determined a radial-coded illumination pattern that could achieve more similar results as sequential scanning and increase the acquisition speed to above 1 Hz. Therefore, this paper provides the possibility of this technique in real-time 3D observation of in vitro live samples.

Analysis, Simulations, and Experiments for Far-Field Fourier Ptychography Imaging Using Active Coherent Synthetic-Aperture

Fourier ptychography (FP) is a powerful phase retrieval method that can be used to reconstruct missing high-frequency details and high-space-bandwidth products in microscopy. In this study, we further advanced the application of FP in microscopic imaging to the field of macroscopic far-field imaging, incorporating camera scanning for spatial resolution improvement. First, on the basis of the Fraunhofer diffraction mechanism and the transmission imaging model, we found the analysis of the associated theoretical fundamentals via simulations and experiments to be crucially relevant to the far-field of FP imaging. Second, we built an experimental device with long-distance imaging and experimentally demonstrated the relationship between the spectrum overlap ratio and the reconstructed high-resolution image. The simulation and experimental results showed that an overlap ratio higher than 50% had a good reconstruction effect. Third, camera scanning was used to obtain low-resolution intensity images in this study, for which the scanning range was wide and spherical wave illumination was satisfied, and therefore different positions corresponded to different aberrations of low-resolution intensity images, and even different positions of the same image had aberration differences, leading to inconsistencies in the aberrations of different images. Therefore, in the reconstruction process, we further overcame the effect of the inconsistency of aberrations of different images using the partition reconstruction method, which involves cutting the image into smaller parts for reconstruction. Finally, with the proposed partition reconstruction algorithm, we were able to resolve 40 μm line width of GBA1 resolution object and obtain a spatial resolution gain of 4× with a working distance of 2 m.

Quantitative Jones matrix imaging using vectorial Fourier ptychography.

This paper presents a microscopic imaging technique that uses variable-angle illumination to recover the complex polarimetric properties of a specimen at high resolution and over a large field-of-view. The approach extends Fourier ptychography, which is a synthetic aperture-based imaging approach to improve resolution with phaseless measurements, to additionally account for the vectorial nature of light. After images are acquired using a standard microscope outfitted with an LED illumination array and two polarizers, our vectorial Fourier ptychography (vFP) algorithm solves for the complex 2x2 Jones matrix of the anisotropic specimen of interest at each resolved spatial location. We introduce a new sequential Gauss-Newton-based solver that additionally jointly estimates and removes polarization-dependent imaging system aberrations. We demonstrate effective vFP performance by generating large-area (29 mm2), high-resolution (1.24 μm full-pitch) reconstructions of sample absorption, phase, orientation, diattenuation, and retardance for a variety of calibration samples and biological specimens.

Cellular analysis using label-free parallel array microscopy with Fourier ptychography.

Quantitative phase imaging (QPI) is an ideal method to non-invasively monitor cell populations and provide label-free imaging and analysis. QPI offers enhanced sample characterization and cell counting compared to conventional label-free techniques. We demonstrate this in the current study through a comparison of cell counting data from digital phase contrast (DPC) imaging and from QPI using a system based on Fourier ptychographic microscopy (FPM). Our FPM system offers multi-well, parallel imaging and a QPI-specific cell segmentation method to establish automated and reliable cell counting. Three cell types were studied and FPM showed improvement in the ability to resolve fine details and thin cells, despite limitations of the FPM system incurred by imaging artifacts. Relative to manually counted fluorescence ground-truth, cell counting results after automated segmentation showed improved accuracy with QPI over DPC.

Using Fourier ptychography microscopy to achieve high-resolution chromosome imaging: an initial evaluation.

.SignificanceSearching analyzable metaphase chromosomes is a critical step for the diagnosis and treatment of leukemia patients, and the searching efficiency is limited by the difficulty that the conventional microscopic systems have in simultaneously achieving high resolution and a large field of view (FOV). However, this challenge can be addressed by Fourier ptychography microscopy (FPM) technology.AimThe purpose of this study is to investigate the feasibility of utilizing FPM to reconstruct high-resolution chromosome images.ApproachAn experimental FPM prototype, which was equipped with or objective lenses to achieve a theoretical equivalent NA of 0.48 and 0.63, respectively, was developed. Under these configurations, we first generated the system modulation transfer function (MTF) curves to assess the resolving power. Next, a group of analyzable metaphase chromosomes were imaged by the FPM system, which were acquired from the peripheral blood samples of the leukemia patients. The chromosome feature qualities were evaluated and compared with the results accomplished by the corresponding conventional microscopes.Results The MTF curve results indicate that the resolving power of the FPM system is equivalent and comparable to the conventional microscope, whereas the performance of the FPM system is close to the conventional microscope. When imaging the chromosomes, the feature qualities of the FPM system are comparable to the results under the conventional lens, whereas the feature qualities of the FPM system are better than the conventional lens and comparable to the conventional lens.ConclusionsThis study initially verified that it is feasible to utilize FPM to develop a high-resolution and wide-field chromosome sample scanner.

Fourier ptychography based on multi-scale feature fusion network

Fourier ptychography based on multi-scale feature fusion network

Optical Transfer Function Measurement Based on Macroscopic Fourier Ptychography

Optical Transfer Function Measurement Based on Macroscopic Fourier Ptychography

Position misalignment correction method for macroscopic Fourier ptychography based on particle swarm optimization

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Accurate and stable two-step LED position calibration method for Fourier ptychographic microscopy.

.Significance: Fourier ptychography microscopy (FPM) is a computational optical imaging technology that employs angularly varying illuminations and a phase retrieval algorithm to achieve a wide field of view and high-resolution imaging simultaneously. In the FPM, LED position error will reduce the quality of the reconstructed high-resolution image. To correct the LED positions, current methods consider each of the LED positions as independent and use an optimization algorithm to get each of the positions. When the positional misalignment is large or the search position falls into a local optimal value, the current methods may lack stability and accuracy.Aim: We improve the model of the LED position and propose an accurate and stable two-step correction scheme (tcFPM) to calibrate the LED position error.Approach: The improved LED positions model combines the overall offset, which represents the relative deviation of the LED array and the optical axis, with the slight deviation of each LED’s independent position. In the tcFPM, the overall offset of the LED array is corrected at first, which obtains an approximate value of the overall offset of the LED array. Then the position of each LED is precisely adjusted, which obtains the slight offset of each LED.Results: This LED position error model is more in line with the actual situation. The simulation and experimental results show that the method has high accuracy in correcting the LED position. Furthermore, the reconstruction process of tcFPM is more stable and significantly improves the quality of the reconstruction results, which is compared with some LED position error correction methods.Conclusions: An LED position error correction technology is proposed, which has a stable iterative process and improves the reconstruction accuracy of complex amplitude.